Question

Aratati ca 1/2x3+1/3x4+1/4x5+...+1/2015x2016< 1/2

Answer 1

1/k*(k+) = 1/k - 1/(k+1

              ⇵

1/2-1/3+1/3-1/4+1/4-1/5+...+1/2015-1/2016 = 1/2-1/2016=1007/2016

        ↑____________________↑

                               =0

Inecuatie de mai sus, se reduce la

 1007/2016 < 1/2   adica:  

1007×2 < 2016×1  ⇔   2014<2016  (A)